Quantum Alternating Operator Ansatz (QAOA) beyond low depth with gradually changing unitaries

• URL: http://arxiv.org/abs/2305.04455v2
• Date: Sat, 22 Jul 2023 04:24:18 GMT
• Title: Quantum Alternating Operator Ansatz (QAOA) beyond low depth with gradually changing unitaries
• Authors: Vladimir Kremenetski, Anuj Apte, Tad Hogg, Stuart Hadfield, and Norm M. Tubman
• Abstract summary: We study the underlying mechanisms governing the behavior of Quantum Alternating Operator Ansatz circuits. We use the discrete adiabatic theorem, which complements and generalizes the insights obtained from the continuous-time adiabatic theorem. Our analysis explains some general properties that are conspicuously depicted in the recently introduced QAOA performance diagrams.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: The Quantum Approximate Optimization Algorithm and its generalization to Quantum Alternating Operator Ansatz (QAOA) is a promising approach for applying quantum computers to challenging problems such as combinatorial optimization and computational chemistry. In this paper, we study the underlying mechanisms governing the behavior of QAOA circuits beyond shallow depth in the practically relevant setting of gradually varying unitaries. We use the discrete adiabatic theorem, which complements and generalizes the insights obtained from the continuous-time adiabatic theorem primarily considered in prior work. Our analysis explains some general properties that are conspicuously depicted in the recently introduced QAOA performance diagrams. For parameter sequences derived from continuous schedules (e.g. linear ramps), these diagrams capture the algorithm's performance over different parameter sizes and circuit depths. Surprisingly, they have been observed to be qualitatively similar across different performance metrics and application domains. Our analysis explains this behavior as well as entails some unexpected results, such as connections between the eigenstates of the cost and mixer QAOA Hamiltonians changing based on parameter size and the possibility of reducing circuit depth without sacrificing performance.

Related papers

• MG-Net: Learn to Customize QAOA with Circuit Depth Awareness [51.78425545377329]
  Quantum Approximate Optimization Algorithm (QAOA) and its variants exhibit immense potential in tackling optimization challenges. The requisite circuit depth for satisfactory performance is problem-specific and often exceeds the maximum capability of current quantum devices. We introduce the Mixer Generator Network (MG-Net), a unified deep learning framework adept at dynamically formulating optimal mixer Hamiltonians.
  arXiv  Detail & Related papers  (2024-09-27T12:28:18Z)
• Connecting the Hamiltonian structure to the QAOA performance and energy landscape [0.0]
  Quantum Alternating Operator Ansatz (QAOA) is effective for solving Quadratic Unconstrained Binary Optimization problems. This study emphasizes the algorithm's robustness and potential for optimization tasks on near-term quantum devices.
  arXiv  Detail & Related papers  (2024-07-05T11:32:46Z)
• Bayesian Parameterized Quantum Circuit Optimization (BPQCO): A task and hardware-dependent approach [49.89480853499917]
  Variational quantum algorithms (VQA) have emerged as a promising quantum alternative for solving optimization and machine learning problems. In this paper, we experimentally demonstrate the influence of the circuit design on the performance obtained for two classification problems. We also study the degradation of the obtained circuits in the presence of noise when simulating real quantum computers.
  arXiv  Detail & Related papers  (2024-04-17T11:00:12Z)
• Exploring the role of parameters in variational quantum algorithms [59.20947681019466]
  We introduce a quantum-control-inspired method for the characterization of variational quantum circuits using the rank of the dynamical Lie algebra. A promising connection is found between the Lie rank, the accuracy of calculated energies, and the requisite depth to attain target states via a given circuit architecture.
  arXiv  Detail & Related papers  (2022-09-28T20:24:53Z)
• Adiabatic Quantum Computing for Multi Object Tracking [170.8716555363907]
  Multi-Object Tracking (MOT) is most often approached in the tracking-by-detection paradigm, where object detections are associated through time. As these optimization problems are often NP-hard, they can only be solved exactly for small instances on current hardware. We show that our approach is competitive compared with state-of-the-art optimization-based approaches, even when using of-the-shelf integer programming solvers.
  arXiv  Detail & Related papers  (2022-02-17T18:59:20Z)
• Parent Hamiltonian as a benchmark problem for variational quantum eigensolvers [0.6946929968559495]
  Variational quantum eigensolver (VQE) finds a ground state of a given Hamiltonian by variationally optimizing the parameters of quantum circuits called ansatz. This work provides a systematic way to analyze energies for VQE and contribute to the design of ansatz and its initial parameters.
  arXiv  Detail & Related papers  (2021-09-24T06:09:10Z)
• Quantum Alternating Operator Ansatz (QAOA) Phase Diagrams and Applications for Quantum Chemistry [0.0]
  We modify QAOA to apply to finding ground states of molecules and empirically evaluate the modified algorithm on several molecules. We find robust qualitative behavior for QAOA as a function of a number of steps and size of the parameters, and demonstrate this behavior also occurs in standard QAOA search.
  arXiv  Detail & Related papers  (2021-08-30T08:24:38Z)
• Parameters Fixing Strategy for Quantum Approximate Optimization Algorithm [0.0]
  We propose a strategy to give high approximation ratio on average, even at large circuit depths, by initializing QAOA with the optimal parameters obtained from the previous depths. We test our strategy on the Max-cut problem of certain classes of graphs such as the 3-regular graphs and the Erd"os-R'enyi graphs.
  arXiv  Detail & Related papers  (2021-08-11T15:44:16Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Adaptive pruning-based optimization of parameterized quantum circuits [62.997667081978825]
  Variisy hybrid quantum-classical algorithms are powerful tools to maximize the use of Noisy Intermediate Scale Quantum devices. We propose a strategy for such ansatze used in variational quantum algorithms, which we call "Efficient Circuit Training" (PECT) Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms.
  arXiv  Detail & Related papers  (2020-10-01T18:14:11Z)
• Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule [0.0]
  We study the problem of estimating the gradient of the function to be optimized directly from quantum measurements. We derive a mathematically exact formula that provides an algorithm for estimating the gradient of any multi-qubit parametric quantum evolution. Our algorithm continues to work, although with some approximations, even when all the available quantum gates are noisy.
  arXiv  Detail & Related papers  (2020-05-20T18:24:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.